University of London

Small Navigation Menu

Primary Menu

Discrete mathematics and algebra MT3170

This course is intended to give an introduction to the areas of mathematics known as discrete mathematics and the study of modern algebra.

A key aim is to provide an insight into the interactions between these areas, in particular to modern applications such as coding and cryptography.

Prerequisite

If taken as part of a BSc degree, courses which must be passed before this courses may be attempted:

  • MT2116 Abstract mathematics.

Topics covered

This full course develops the mathematical methods of discrete mathematics and algebra and will emphasis their applications.

  • Counting: selections, inclusion-exclusion, partitions and permutations, Stirling numbers, generating functions, recurrence relations.
  • Graph Theory: basic concepts (graph, adjacency matrix, etc.), walks and cycles, trees and forests, colourings.
  • Set Systems: matching, finite geometries, block designs.
  • Abstract groups: revision of key concepts such as cyclic groups, subgroups, homomorphisms and Lagrange’s theorem. Conjugation and normal subgroups. Group actions.
  • Applications of algebra to discrete mathematics I: permutations, orbits and stabilisers, the orbit-stabiliser theorem; applications to counting problems.
  • Rings and polynomials: the Euclidean algorithm for polynomials, integral domains, ideals, factor rings, fields, field extensions.
  • Finite fields: construction, the primitive element theorem, and finite linear algebra.
  • Applications of algebra to discrete mathematics II: finite Geometry: designs, affine and projective planes.
  • Error-correcting codes: linear codes, cyclic codes, perfect codes.

Learning outcomes

If you complete the course successfully, you should be able to:

  • Demonstrate knowledge definitions, concepts and methods in the topics covered and how to apply these
  • Find and formulate simple proofs
  • Model situations in a mathematical way and derive useful results.

Assessment

Unseen written exam (3 hrs).

Essential reading

  • Biggs, N. Discrete mathematics. Oxford: Oxford University Press, 2002.
  • Cameron, P.J. Introduction to Algebra. Oxford: Oxford University Press, 2008.
  • Cameron, P.J. Combinatorics. Oxford: Oxford University Press, 2008.

Course information sheets

Download the course information sheets from the LSE website.